抄録
The realization problem of pseudo-linear systems had been presented with the following realization theorem.
Realization theorem ⌈For any invariant input-response map (equivalently, any input/output map with causality and time-invariance), there exist at least two canonical pseudo-linear systems which realize it. Moreover any two canonical pseudo-linear systems with same behavior are isomorphic each other.⌋ Where electric circuits with FET transistors are examples of pseudo-linear systems. Moreover, the finite-dimensionality of pseudo-linear systems had been discussed.
In this paper, being based on the ubove results, we will discuss problems of the partial and real-time partial realization. The problems can be roughly described as the follows. The partial realization problem ⌈For a given partial time-invariant input response map by multi-experiments, find uniquely a minimal dimensional pseudo-linear system which partially realizes it. The real-time partial realization problem ⌈For a given partial time-invariant input response map by single-experiment, find uniquely a minimal dimensioal pseudo-linear system which partially realizes it. And the following results are obtained.
(1) A necessary and sufficient condition for minimal partial realization systems to be unique is given by the rank condition of input/output matrix.
(2) For a given partial time-invariant input response map by multi-experiments, an algorithm to obtain the minimal partial realization system is given.
(3) For a given partial time-invariant input response map by single-experiment, an algorithm to obtain the minimal realization system is given.
We conclude that these results about partial realization are the extention of the finite-dimensional, constant, linear systems to a non-linear system.
